Table 1.

Within- and between-host model variables and parameters

Notations
t	Time
$\tau$	Time since infection (infection age)
x	Resistance level
i	host immune response level
Model state variables
Within-host
$b_i^T(\tau ,x)$	Bacteria density with resistance level x at time $\tau$ in a treated host
$b_i^U(\tau ,x)$	Bacteria density with resistance level x at time $\tau$ in an untreated host
Between-host
$S_i(t)$	Susceptible humans at time t
$I_i^T(t,\tau )$	Treated infected humans, infected since time $\tau$
$I_i^U(t,\tau )$	Untreated infected humans, infected since time $\tau$
Model parameters
Within-host
$\kappa$	Limitation on bacterial growth factor
$J(x-y)$	Mutation probability from resistance level x to y per cell division
p(x)	Intrinsic growth rate of bacterial population with resistance level x
k(x)	Killing rate of bacterial population with resistance level x due to drug
${\mu }_i(x)$	Individual clearance rate of the bacterial cell with resistance level x due to the immune response
${\xi }_i^U(x)={\mu }_i(x)$	Bacteria clearance rate with resistance level x in untreated hosts
${\xi }_i^T(x)=k(x)+{\mu }_i(x)$	Bacteria clearance rate with resistance level x in treated hosts due to the immune response and drug
Between-host
${\beta }_i^{\vartheta }(\tau )$, $\vartheta \in \{T,U\}$	Transmission rate of infected individuals
${\alpha }_i^{\vartheta }(\tau )$, $\vartheta \in \{T,U\}$	Loss rate of infected individuals
${\omega }_U^T(\tau )$	Rate of treatment cessation
${\omega }_T^U(\tau )$	Rate of treatment start
$q_i^T$	Proportion of treated hosts
$q_i^U=1-q_i^T$	Proportion of untreated hosts
${\mathrm{\Lambda }}_i$	Recruitment rate of susceptibles
${\mu }_h$	Human natural death rate